PROCEDURE for the dough1. In the bowl of a food processor fitted with the blade attachment, pulse together the flour, cornstarch, sugar, and salt. Add the butter and pulse until the mixture resembles coarse cornmeal.2. In a small bowl, whisk together the egg, condensed milk and vanilla. Slowly add the egg mixture to the flour mixture while pulsing; continue until the dough just begins to come together.3. Turn the dough out onto a lightly floured surface. Gently knead it until the dry ingredients are fully integrated and the dough holds together, being careful not to overwork it.4. Form the dough into a disk, wrap it in plastic, and refrigerate it for at least 30 minutes.

Procedure for the crust1. Preheat the oven to 350 degrees. Press the dough into a 9" square or round tart pan and freeze it for 20 minutes. Line the tart pan with parchment and fill with pie weights or dried beans. Bake the crust for 15 minutes.2. Remove the crust from the oven; remove the pie weights and parchment. Brush the crust with the apricot preserves and bake it for another 5 minutes. Set aside.

Procedure for the filling1. In a large saucepan, melt the butter along with 1/4 cup of the granulated sugar, the lemon zest and juice, and the rum. Add the apple slices and sauté until just tender. Remove the apple slices with a slotted spoon, leaving the juiced in the pan.2. Add the cream, remaining granulated sugar, vanilla, and salt to the saucepan. Bring the mixture to a simmer.3. In the meantime, whisk the eggs in a mixing bowl. Continuing to whisk, slowly pour the hot cream mixture in a steady stream into the eggs.

Assembly1. Arrange the apples slices evenly on the crust, overlapping them slightly. Pour the custard over the apples. Carefully transfer the tart to the oven and bake it until the custard has set and the edges are slightly golden, 30 to 35 minutes.2. In a small bowl, stir together the confectioner's sugar and cream until smooth. Allow the tart to cool slightly and using a pastry brush, gently brush the top of the apples with the sugar glaze. Allow the tart to cool completely , then carefully remove it from the tart pan and transfer it to a platter. Serve with slightly sweetened whipped cream.